We next consider the optimal values of the response parameters. In the adaptive response, \(\tau \)  (the memory length) is very short (Table REF ), allowing the bacterium to quickly adjust to small displacements from attractant optima. \(\beta \) , the rate at which the bacterium stops tumbling, is quite large, corresponding to short-lasting tumbles characteristic of chemotaxis in E. coli [1]}. High sensitivity (large \(|A|\)  and \(|B|\) ) is necessary for the bacterium to respond to small differences in attractant concentration characteristic of small displacements from the top of an attractant peak. High sensitivity is responsible for the high \(\alpha \)  when the attractant is removed at \(t = 350\)  in Fig. REF c (red curve). Optimal \(\alpha _0\) , the tumbling rate in the absence of attractant (or under constant attractant in case of perfect adaptation), is very low in all strategies, as is evident from Fig. REF c. Low \(\alpha _0\)  enables bacteria to run persistently in order to find regions with more favorable conditions more quickly. The near-zero value of \(\alpha _0\)  removes the possibility of \(\alpha \)  going below \(\alpha _0\) , eliminating the response to increasing attractant in the adaptive response (Figure REF c, red curve, \(t = 50\) ).
